Problem: What do the following two equations represent? $-5x+5y = 3$ $-5x-5y = 3$
Answer: Putting the first equation in $y = mx + b$ form gives: $-5x+5y = 3$ $5y = 5x+3$ $y = 1x + \dfrac{3}{5}$ Putting the second equation in $y = mx + b$ form gives: $-5x-5y = 3$ $-5y = 5x+3$ $y = -1x - \dfrac{3}{5}$ The slopes are negative inverses of each other, so the lines are perpendicular.